CompTIA Data+ (DA0-002)Data AnalysisHard
A market researcher is conducting a survey to estimate the average spending of customers in a particular demographic. They collect data from a sample and calculate a 95% confidence interval for the mean spending. This interval is ($120, $150). What does this interval imply?
- AThe probability that a randomly selected customer spends between $120 and $150 is 95%.
- BThere is a 95% probability that the true population mean spending is exactly $135.
- CIf the survey were repeated many times, 95% of the calculated confidence intervals would contain the true population mean spending.
- D95% of customers in the sample spent between $120 and $150.
Show answer & explanationAnswer & explanation
Correct answer: C. If the survey were repeated many times, 95% of the calculated confidence intervals would contain the true population mean spending.
A 95% confidence interval means that if we were to repeat the sampling process and construct a confidence interval many times, approximately 95% of those intervals would contain the true population parameter (in this case, the mean spending). It is not about the probability of the true mean being within a specific interval or the percentage of individual data points within the interval.
Why the other options are wrong
- A. This is an interpretation about individual customer spending, not about the confidence in the estimate of the population mean.
- B. The confidence interval does not state the probability of the true mean being a single exact value, nor does it imply the true mean is fixed at the midpoint.
- D. This describes a range for individual data points, not the confidence interval for the population mean.
Confidence Interval
A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter.
- Expressed with a confidence level (e.g., 90%, 95%, 99%).
- Indicates the reliability of an estimate.
- Wider intervals indicate greater uncertainty.
Memory trick: CI: How CONFIDENT are we that our NET catches the true mean?